Question

two capacitors c1 and c2 are connected in series with a voltage v across the combination. show that the voltage v1 and v2 across c1 and c2,respectively are: v1=c2/c1+c2 and v2=c1/c1+c2

Answer 1

We know, q=CV
Therefore, V=q/C
Here, V1=q/C1 and V2=q/C2 (when two capacitors are connected in series they store equal amount of charges)
So, q=C1V1=C2V2
Now, V1+V2=V
By putting the value V2=V-V1 we get
C1V1=C2(V-V1)
=>C1V1=C2V-C2V1
=>V1(C1+C2)=C2V
=> V1=C2V/(C1+C2) (proved)
Similarly, By putting the value V1=V-V2 we get
C2V2=C1(V-V2)
=>C2V2=C1V-C1V2
=>V2(C1+C2)=C1V
=> V2=C1V/(C1+C2) (proved)
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